代写 R C matlab ENG104 MATLAB Assignment

ENG104 MATLAB Assignment
Due 5pm 4/10/19
1. Consider the RL circuit shown in Figure 1.
(a) [1 mark] Determine an ODE for the current i 􏰂owing through the inductor.
(b) [1 marks] Approximate the derivative as
di ∼= i(t+δt)−i(t)
dt δt
to get a recursive equation for i(t + δt) in terms of i(t).
(c) [2 marks] Write a MATLAB script RLPlotter1c that uses the result of 1(b) to compute and plot ifort∈[0,T]. UsevaluesofR=1Ω,L=2H,T =10s,Vs =10V,i(0)=0A,andδt=0.1s. Ensure that the axis labels are labeled.
(d) [2 marks] Write a MALTAB function RLSolver that takes six inputs and returns two outputs. The inputs should be the values of R, L, T, Vs, i(0), and δt. The 􏰁rst output should be a vector containing the values of t and the second output should be a vector containing the corresponding values of i(t). (You should be able to reuse code from the previous question for this).
(e) [2 marks] Write a MATLAB script RLPlotter1e that makes use of RLSolver to produce a plot showing i(t) for δt = 0.01s, δt = 0.1s, and δt = 1s (all other parameters are as given in 1(c)). Ensure the plot contains axis labels as well as a legend.
(f) [2 marks] Write a MATLAB script RLPlotter1f that makes use of RLSolver to produce a plot showing i(t) for all four possible combinations of R = 1 Ω or R = 2 Ω and L = 1 H or L = 2 H (all other parameters are as given in 1(c)). Ensure the plot contains axis labels as well as a legend.
R
+
Vs
i
L
−
Figure 1: RL circuit.
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2. Now consider the RLC circuit shown in Figure 2.
(a) [2 marks] Determine an ODE for the current i 􏰂owing through the inductor.
(b) [1 marks] Make the substitution ψ(t) = di to convert the second order ODE into a pair of single dt
order ODEs.
(c) [2 marks] Approximate the derivatives as
di ∼= i(t+δt)−i(t),
dt δt
dψ ∼= ψ(t+δt)−ψ(t) dt δt
to get a pair of recursive equations for i(t + δt) and ψ(t + δt) in terms of i(t) and ψ(t).
(d) [3 marks] Write a MATLAB function RLCSolver that takes eight inputs and returns two outputs. The inputs should be the values of R, L, C, T, Vs, i(0), ψ(0), and δt. The 􏰁rst output should be a vector containing the values of t and the second output should be a vector containing the corresponding values of i(t).
(e) [2 marks] Write a MATLAB script RLCPlotter2e that makes use of RLCSolver to produce a plot showing i(t) for C = 1F, T = 20s, Vs = 10V, i(0) = 0A, ψ(0) = 0As−1, δt = 0.1s and all four possible combinations of R = 1Ω or R = 2Ω and L = 1H or L = 2H. Ensure the plot contains axis labels as well as a legend. Note that the current should converge to the same value as in the RL circuit for t → ∞.
R
Vs+ C −
Figure 2: RLC circuit.
i
L
Submission guidelines
• Your MATLAB scripts and functions should all be di􏰀erent 􏰁les (please use the suggested names).
• Your answers to 1(a), 1(b), 2(a), 2(b), and 2(c) can either be in a single 􏰁le or multiple 􏰁les. Typed or scanned handwritten answers are both 􏰁ne.
• Include all 􏰁les in a single zip 􏰁le and submit on MyLO. Please include your name and student number in the name of the zip 􏰁le.
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